E is a high-performance theorem prover for full first-order logic with equality. It is based on the equational superposition calculus and uses a purely equational paradigm. It has been integrated into other theorem provers and it has been among the best-placed systems in several theorem proving competitions. E is developed by Stephan Schulz, originally in the ''Automated Reasoning Group'' at

TU Munich The Technical University of Munich (TUM or TU Munich; german: Technische Universität München) is a public research university in Munich, Germany. It specializes in engineering, technology, medicine, and applied and natural sciences. Establis ...

, now at Baden-Württemberg Cooperative State University Stuttgart.

System

The system is based on the equational superposition calculus. In contrast to most other current provers, the implementation actually uses a purely equational paradigm, and simulates non-equational inferences via appropriate equality inferences. Significant innovations include shared term rewriting (where many possible equational simplifications are carried out in a single operation), several efficient

term indexing In computer science, a term index is a data structure to facilitate fast lookup of terms and clauses in a logic program, deductive database, or automated theorem prover. Overview Many operations in automatic theorem provers require search in hu ...

data structures for speeding up inferences, advanced inference literal selection strategies, and various uses of machine learning techniques to improve the search behaviour. Since version 2.0, E supports

many-sorted logic Many-sorted logic can reflect formally our intention not to handle the universe as a homogeneous collection of objects, but to partition it in a way that is similar to types in typeful programming. Both functional and assertive "parts of speech" i ...

. E is implemented in C and portable to most

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variants and the

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environment. It is available under the

GNU GPL The GNU General Public License (GNU GPL or simply GPL) is a series of widely used free software licenses that guarantee end users the four freedoms to run, study, share, and modify the software. The license was the first copyleft for general us ...

Competitions

The prover has consistently performed well in the

CADE ATP System Competition The CADE ATP System Competition (CASC) is a yearly competition of fully automated theorem provers for classical logic CASC is associated with the Conference on Automated Deduction and the International Joint Conference on Automated Reasoning organi ...

, winning the CNF/MIX category in 2000 and finishing among the top systems ever since. In 2008 it came in second place. In 2009 it won second place in the FOF (full first order logic) and UEQ (unit equational logic) categories and third place (after two versions of

Vampire A vampire is a mythical creature that subsists by feeding on the Vitalism, vital essence (generally in the form of blood) of the living. In European folklore, vampires are undead, undead creatures that often visited loved ones and caused mi ...

) in CNF (clausal logic). It repeated the performance in FOF and CNF in 2010, and won a special award as "overall best" system. In the 2011 CASC-23 E won the CNF division and achieved second places in UEQ and LTB.

Applications

E has been integrated into several other theorem provers. It is, with

, SPASS
CVC4
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Z3
at the core of

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's ''Sledgehammer'' strategy. E also is the reasoning engine in SInE and LEO-II and used as the clausification system for iProver. Applications of E include reasoning on large ontologies, software verification, and software certification.

References

External links

E home page
{{DEFAULTSORT:E Theorem Prover Free software programmed in C Free theorem provers Unix programming tools